Latrell Sprewell is relieved that his 1999-2000 season hasn’t been filled with the phrase “free-agent-to-be” attached to his name.

So are the Knicks. Can you imagine if Garden prez Dave Checketts and Knicks’ GM Scott Layden had held a grudge and not come up big in October?

The Knicks’ brass flew to Buffalo during the preseason and presented Sprewell with a fill-in-the-blanks, maximum-contract extension only two weeks after Sprewell ticked off the higher-ups and Jeff Van Gundy. Spree had been docked $130,000 for skipping the six-day Charleston, S.C., training camp after he drove cross-country following his civil trial in California.

Either Spree would have been traded at the Feb. 23 deadline or the Knicks would be looking mighty foolish, especially now that his stock is soaring through the Garden ceiling after outclassing “the Next Jordan” in the first two first-round playoff games.

Sprewell chose to accept a five-year, $62.8 million deal with an out after four years. Spree could have waited for the summer and qualified for a larger maximum deal under the CBA. But everybody is ecstatic now.

“It’s why I did it early,” Sprewell said. “I didn’t want to have to deal with it. There would be so much talk going on if I was going to stay or go. It’s obvious I want to be here. I felt that way at the beginning of the year. I just didn’t want to have to deal with that during the season.”

Sprewell credits Checketts, who said as early as an August news conference introducing Layden that he wanted to lock up Spree long-term. Checketts put aside his well-documented differences with Spree’s outspoken agent, Bob Gist, and moved forward, even though it’s known they still got into a nasty argument during the October negotiating session in Buffalo that nearly blew the deal up. (Last season, Checketts fined Sprewell $25,000 for inflammatory remarks his agent made about the organization).

“He’s the guy who wanted it to happen,” said Sprewell of Checketts. “I felt comfortable being here and once he knew that I wanted to be here and stay, he committed himself and the organization to me. At that point, why wait?”

After the offer, Sprewell spent a few days debating whether to go with a short-term deal or long-term. He could have maximized his overall income by going with a two-year extension, then signing an even more lucrative deal next time around. He went long-term, not wanting to take the risk.

“I’m happy with the contract the way it is,” Sprewell said. “We hashed out the numbers. I could live with what I got.”

Sprewell lived last season at a Residence Inn in White Plains. Had he not gotten an extension, he could have remained there this season. With the contract in place, Sprewell bought a house in White Plains and moved out of the hotel in January. He was joined by his fiancee from Milwaukee and his infant son, who was born right before training camp.

“It’s beautiful,” Sprewell said of his house. “Comfortable. [New York] feels more like home.”

Before the playoffs began, the NBA approached Knicks public relations chief Lori Hamamoto and, of all the players, requested Sprewell to do a playoff promotional commercial. So much for the P.J. Carlesimo choking incident.

“It was nice,” Sprewell said. “Any time you’re given a chance to be put in a commercial, it was flattering and coming from those guys, whom I haven’t had a great relationship with, says a lot more. It’s been a couple of years now. I think people have moved on.”

Asked what commissioner David Stern must be thinking now that Sprewell is outshining league golden-boy Carter, Spree said modestly, “I’m not outplaying Vince. Vince has faced pretty good team defense. I don’t know what Stern is thinking.”